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arXiv · 1205.5631

Vertex decomposable graphs, codismantlability, Cohen-Macaulayness and Castelnuovo-Mumford regularity

Turker Biyikoglu·Yusuf Civan
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Abstract

We call a (simple) graph G codismantlable if either it has no edges or else it has a codominated vertex x, meaning that the closed neighborhood of x contains that of one of its neighbor, such that G-x codismantlable. We prove that if G is well-covered and it lacks induced cycles of length four, five and seven, than the vertex decomposability, codismantlability and Cohen-Macaulayness for G are all equivalent. The rest deals with the computation of Castelnuovo-Mumford regularity of codismantlable graphs. Note that our approach complements and unifies many of the earlier results on bipartite, chordal and very well-covered graphs.

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Turker Biyikoglu, Yusuf Civan. 2014-01-21. Vertex decomposable graphs, codismantlability, Cohen-Macaulayness and Castelnuovo-Mumford regularity. https://arxiv.org/abs/1205.5631

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